A complete classification of bifurcation diagrams of a p-Laplacian Dirichlet problem

We study the bifurcation diagrams of classical positive solutions u with u ∞ ∈ (0,∞) of the p-Laplacian Dirichlet problem ϕp u (x) +λfq u(x) = 0, −11, ϕp(y) = |y|p−2y, (ϕp(u )) is the one-dimensional p-Laplacian, λ>0 is a bifurcation parameter, and fq (u) = |1 − u|q is defined on [0,∞) with q >0. More precisely, for different (p, q), we give a complete classification of bifurcation diagrams of classical positive solutions on the (λ, u ∞)-plane. Hence we are able to determine the exact multiplicity of classical positive solutions for each (p, q,λ). © 2006 Elsevier Inc. All rights reserved.